Trigonometry PDT

Convert  $\frac{\pi}{4}$  rad into degree ?

• 30

• 45

• 60

• 90

What is acute angle ?

• $0^{\degree}<\theta<90^{\degree}$

• $90^{\degree}<\theta<180^{\degree}$

• $180^{\degree}<\theta<270^{\degree}$

• $270^{\degree}<\theta<360^{\degree}$

Find  $\cos\theta$  ?

•  $\frac{y}{x}$  

•  $\frac{x}{y}$  

•  $\frac{y}{r}$ 

•  $\frac{x}{r}$  

•  $\frac{r}{x}$  

What is  $\operatorname{cosec}\theta$  ?

•  $\frac{r}{x}$  

•  $\frac{x}{r}$  

•  $\frac{y}{r}$  

•  $\frac{r}{y}$  

•  $\frac{x}{y}$  

If  $\cos\theta=\frac{3}{5}$  and  $\theta$  is situated at fourth quadrant, find  $\cot\ \theta$  ?

•  $\frac{5}{3}$  

•  $\frac{1}{2}$  

•  $-\frac{3}{4}$  

•  $\frac{3}{4}$  

•  $-\frac{4}{3}$  

What is obtuse angle ?

• $270^{\degree}<\theta<360^{\degree}$

• $180^{\degree}<\theta<270^{\degree}$

• $90^{\degree}<\theta<180^{\degree}$

• $0^{\degree}<\theta<90^{\degree}$

Find the trigonometric ratio of $\tan\left(-150^{\degree}\right)$  ?

•  $\frac{1}{\sqrt{3}}$  

•  $-\sqrt{3}$  

• 1

•  $3\sqrt{3}$  

•  $\frac{\sqrt{3}}{3}$  

Solve $\cos\theta=-0.5$  for  $0^{\degree}<\theta<360^{\degree}$  .

•  $\theta=30^{\degree}\ ,\ 120^{\degree}$  

•  $\theta=60^{\degree},\ 120^{\degree}$  

•  $\theta=60^{\degree}\ ,\ 300^{\degree}$  

•  $\theta=120^{\degree}\ ,\ 240^{\degree}$  

•  $\theta=120^{\degree}\ ,\ 300^{\degree}$  

Which one of the trigonometric identities below are false ?

• $\cos^2\theta=1-\sin^2\theta$

• $1=\operatorname{cosec}^2\theta-\cot^2\theta$

• $\tan^2\theta=\sec^2\theta-1$

• $\operatorname{cosec}^2\theta=\cot^2\theta-1$

Solve $4\cos^2\theta\ +\ 5\sin\theta=5$  for  $0^{\degree}\le\theta\le180^{\degree}$  .  (Hint : use suitable trigonometric identities.)

•  $\theta\ =\ 14.5^{\degree}\ ,\ 50^{\degree}\ ,\ 175.5^{\degree}$  

•  $\theta=60^{\degree}\ ,\ 90^{\degree}\ ,\ 165.5^{\degree}$  

•  $\theta=14.5^{\degree}\ ,\ 90^{\degree}\ ,\ 165.5^{\degree}\ ,\ 270^{\degree}$  

•  $\theta=60^{\degree},\ 90^{\degree},\ 120^{\degree}$  

•  $\theta=14.5^{\degree}\ ,\ 90^{\degree}\ ,\ 165.5^{\degree}$